Thermal applicability of two-phase thermosyphons in ... - LEPTEN

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730 A.K. da Silva, M.B.H. Mantelli / Applied Thermal Engineering 24 (2004) 717–7331000Theoretical resultsExperimental measurementT 4100100 1800 3600 5400 7200tFig. 10. Bottom surface temperature variation (T 4 )––experimental and theoretical comparison.It should be noted that the characteristic velocities were not measured. Several theoretical valueswere used in the model with the objective of getting a curve that presents a good comparison withthe data. This good comparison obtained was always obtained for low velocities (i.e., v 6 2ms 1 )showing that the convection heat transfer, which is proportional to the air velocity flowing over asurface inside the chamber, does not play the major role. The greatest part of the heat is transferredby radiation. It should be noted that Figs. 9 and 10 show a better agreement between thetheoretical results and experimental measurements than Fig. 8. This happens because the temperatureof the air inside the chamber is completely heated by convection. On the other hand, theinternal walls receive energy by radiation, which was precisely determined by the theoreticalmodel.To better illustrate this point, Fig. 11 shows the dimensionless contribution of the radiative heatflux (i.e., ^q rad ¼ q rad =q Total ), and convective heat flux (i.e., ^q conv ¼ q conv =q Total ), where q Total ¼ q conv þq rad . In other words, the vertical axis represents the convective or the radiative fraction of energyheat flux leaving the thermosyphonsÕ condenser. The horizontal axis is the dimensionless time^t ¼ at=H 2 , where a is defined as the air thermal diffusivity, t is the time and H is the characteristicsurface length (i.e., condenser length). Several curves were plotted for different wall emissivities. Itcan be observed that for the initial time ^t ¼ 0, all the curves are close together and for everyinstant with a fixed wall emissivity, the sum of the dimensionless radiative and convective heat fluxis equal to 1. As the time goes by, the walls and the air are being heated up by convection atdifferent rates. For e ¼ 0:9, the difference between the radiation and convection is more evidentdue to the high amount of energy that the walls are able to absorb by radiation. In this case, mostof the energy that reaches the internal walls is absorbed by radiation and transferred by convectionto the enclosed air. The higher the internal wall emissivity, the faster the thermal responseof the internal walls and consequently the smaller the convection heat transfer, which is stronglyrelated with the temperature of the air inside. For e ¼ 0:9, the radiative heat flux represents about
A.K. da Silva, M.B.H. Mantelli / Applied Thermal Engineering 24 (2004) 717–733 731qˆ rad1qˆ radε =0.90.50.20.5ε =0.2qˆ convqˆ conv0.50.900 100 200 300 400 500 600 700tFig. 11. Theoretical convective and radiative dimensionless heat flux.90% of the total energy exchanged within the enclosure, and the convective heat flux representsabout 10%. This analysis implies that the radiation heat transfer primarily dominates the heattransfer in a cooking chamber. Assuming the internal walls with e ¼ 0:2 (i.e., which is approximatelythe order of magnitude of polish steel commonly used inside ovens), Fig. 11 shows thatmost of the energy emitted by radiation from the vertical walls is reflected within the internalwalls, delaying the walls and the inside air heating up process. For e ¼ 0:2, the radiation represents65% of the total energy that enters within the enclosure. For the intermediate value ofemissivity, e ¼ 0:5, the radiation suppresses the convection heat flux by a factor of 4. Similarcurves could be plotted for the other surfaces, but they will not be presented here.These are very interesting results that can lead to important conclusions with respect to thethermal applicability of thermosyphons in cooking chambers, specially if we consider a real situationwhere any unbaked product is placed inside the oven/furnace. By associating the experimentaltemperature distribution shown in Fig. 7 with the heat transfer modes shown in Fig. 11, itis reasonable to conclude that the thermosyphon are consistently eligible for such application. Thereason for that stems from the fact that any unbaked product will bake uniformly when exposedto such an approximately uniform temperature distribution environment (Fig. 7), and, at the sametime, to a uniform radiation network at low temperature (i.e., T hot wall ffi T air ) provided by thesurrounding hot walls (i.e., thermosyphonsÕ condensers).6. ConclusionsIn the present work we designed and built an experimental prototype to investigate theapplicability of thermosyphons as heat transfer devices in ovens or furnaces. The experimental
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Thermal applicability of two-phase thermosyphons in ... - LEPTEN

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